No coincidence of center percolation and deconfinement in SU(4) lattice gauge theory

Abstract

We study the behavior of center sectors in pure SU(4) lattice gauge theory at finite temperature. The center sectors are defined as spatial clusters of neighboring sites with values of their local Polyakov loops near the same center elements. We study the connectedness and percolation properties of the center clusters across the deconfinement transition. We show that for SU(4) gauge theory deconfinement cannot be described as a percolation transition of center clusters, a finding which is different from pure SU(2) or pure SU(3) Yang Mills theory, where the percolation description even allows for a continuum limit.

Center clusters in full QCD at finite temperature and background magnetic field

“…Although the expectation value of P is -due to the explicit breaking -always real, it turns out that there are local domains in space, in which the Polyakov loop points towards one of the three center sectors [17][18][19][20][21][22][23][24][25]. The corresponding local Polyakov loops L(x) read…”

“…1) and induces a large real average Polyakov loop. This picture of center clusters has been studied in pure gauge theory with two [17,18], with three [9,19,20] and with four colors [21], while preliminary results for dynamical quarks have been obtained in Refs. [22,23].…”

“…[24,25].) We mention that while the change in the distribution of arg L(x) is essential for the deconfinement transition, the modulus |L(x)| was found to play no relevant role in this respect [17][18][19][20][21][22][23][24].…”

“…Thus, such clusters become infinitely large in the infinite volume limit.) The simplest choice reflecting the abrupt change of gluonic configurations in this respect is the percolation probability p ∞ [9,19,[21][22][23]. It is defined as the probability of having a percolating cluster and is thus bounded 2 Note that this direct realization of the Svetitsky-Yaffe conjecture becomes considerably more involved for SU(N ) theories with N ≥ 4.…”

“…Unlike for SU(3) -where the Polyakov loop effective action is constructed exclusively via L(x) of Eq. (3) -for SU(4), it involves the trace of gauge links in representations with different dimensions (4 and 6) [21,38,39]. The 4-dimensional representation alone was shown to be insufficient to describe the deconfinement transition via percolation, since the clusters were found to become too thin towards the continuum limit [21].…”